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Static thermoelasticity problems for layered thermosensitive plates with cubic dependence of the coefficients of heat conductivity on temperature

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We describe an analytic-numerical method of solution of one-dimensional static thermoelasticity problems for layered plates, heated in different ways. We take into account the cubic dependence of the coefficients of heat conductivity and arbitrary nature of the dependence of other physicomechanical parameters on temperature. Here, using the constructed exact solution of an auxiliary problem, we have reduced the heat conduction problems, irrespective of the number of layers, to the solution of one or a system of two nonlinear algebraic equations. We have also studied the temperature fields and stresses in four-layer plates under conditions of complex heat exchange.

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    Yu. B. Protsyuk

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  1. Yu. B. Protsyuk
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 53, No. 4, pp. 151–161, October–December, 2010.

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Protsyuk, Y.B. Static thermoelasticity problems for layered thermosensitive plates with cubic dependence of the coefficients of heat conductivity on temperature. J Math Sci 181, 481–496 (2012). https://doi.org/10.1007/s10958-012-0700-z

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  • DOI: https://doi.org/10.1007/s10958-012-0700-z

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